Why is the base of the object fading in and out during rendering?
The 'fading' is actually just blurring from the vector blur node in the compositor.

If you wish to remove this effect, you can either just disable the Vector Blur node by pressing M while the node is selected in the compositor to 'Mute' the node or you could press Ctrl+X to essentially 'Cut' the node out. In future, you can use the technique of muting nodes one by one to diagnose issues with node setups.

If you remove the Vector Blur node you may be able to remove more nodes, such as the Alpha Over node the Vector Blur connects to and even the 'Foreground' render layer (as it may be the only purpose of this render layer is for the Vector Blur).